| The paradigm of model evaluation is challenged by compensations between various forms of errors and uncertainties that are inherent to the model development process due to, for instance, imprecise model input parameters, scarcity of experimental data and lack of knowledge regarding an accurate mathematical representation of the system. When calibrating model input parameters based on fidelity to experiments, such compensations lead to non-unique solutions. In turn, the existence of non-unique solutions makes the selection and use of one `best' numerical model risky. Therefore, it becomes necessary to evaluate model performance based not only on the fidelity of the predictions to experiments but also the model's ability to satisfy fidelity threshold requirements in the face of uncertainties. The level of inherent uncertainty need not be known a priori as the model's predictions can be evaluated for increasing levels of uncertainty, and a model form can be sought that yields the highest probability of satisfying a given fidelity threshold. By implementing these concepts, this manuscript presents a probabilistic formulation of a robust-satisfying approach, along with its associated metric. This new formulation evaluates the performance of a model form based on the probability that the model predictions match experimental data within a predefined fidelity threshold when subject to uncertainty in their input parameters. This approach can be used to evaluate the robustness and fidelity of a numerical model as part of a model validation campaign, or to compare multiple candidate model forms as part of a model selection campaign. In this thesis, the conceptual framework and mathematical formulation of this new probabilistic treatment of robust-satisfying approach is presented. The feasibility and application of this new approach is demonstrated on a structural steel frame with uncertain connection parameters, which has undergone static loading conditions. |
